The radii of two concentric circles are 34 cm and 50 cm. A and D are the points on larger circle and B and C are points on smaller circle. If ABCD is a straight line and BC = 32 cm, then what is the length of AD?
Answer & explanation
Correct answer: option 2
BC = 32 cm
BP = \(\frac{32}{2}\) = 16 cm
In triangle OBP
Apply pythagoras theorem
\( {OB }^{2 } \) = \( {BP }^{2 } \) + \( {OP }^{2 } \)
\( {34 }^{2 } \) = \( {OP }^{2 } \) + \( {16 }^{2 } \)
\( {OP }^{2 } \) = 1156 - 256
\( {OB }^{2 } \) = 900
OP = 30 cm
In triangle OPD
\( {OD }^{2 } \) = \( {OP }^{2 } \) + \( {PD }^{2 } \)
= \( {50 }^{2 } \) = \( {30 }^{2 } \) + \( {PD }^{2 } \)
= \( {PD }^{2 } \) = 2500 - 900
= \( {PD }^{2 } \) = 1600
= PD = 40 cm
= AD = 2 x PD = 2 x 40 = 80 cm
Therefore, the length of AD is 80 cm.